Open AccessCertain properties of rational functions involving Bessel functions
Author(s) -
Rasoul Aghalary,
Ali Ebadian,
Zahra Oroujy
Publication year - 2012
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.43.2012.814
Subject(s) - bessel function , mathematics , order (exchange) , rational function , beta (programming language) , combinatorics , function (biology) , unit (ring theory) , operator (biology) , mathematical analysis , mathematical physics , pure mathematics , chemistry , biochemistry , mathematics education , finance , repressor , evolutionary biology , computer science , transcription factor , gene , economics , biology , programming language
Let $g_{upsilon}(z)$ be the classical Bessel function of the first kind of order $upsilon$ and $f$ be an analytic function defined on the unit disc $Delta$. Suppose the operator $H(f)$ be defined by $H(f)(z)=frac{z}{frac{z}{f(z)}*frac{g_{upsilon}(z)}{z}}$. In this paper we identify subfamily $M_{n}(alpha,eta)$ of univalent functions and obtain conditions on the parameter $upsilon$ such that $fin M_{n}(alpha,eta)$ implies $H(f)in M_{n}(alpha,eta)$